This invention relates generally to rotating induction apparatus and more specifically to more efficient rotating induction apparatus. It relates to pulse width modulation (PWM), and the synthesis of desired alternating current for motor drive applications.
Electric motors in operation make use of the fact that a current of charge in a magnetic field will experience a force perpendicular to both the current and the field. In the case of the AC induction motor, a set of energized windings, the stator windings, produce a rotating magnetic field. This rotating magnetic field induces current in a set of rotatable windings, the rotor windings. Additionally, this rotating magnetic field interacts with the rotor current, and causes the rotor to turn. Ideally, the rotating magnetic field will have a fixed spatial structure, simply changing orientation at a suitable rate.
In a three-phase induction motor, the magnetic field has a sinusoidal distribution. This means that on a particular point on the interface between the rotor and the stator, also known as the ‘air gap’, the magnetic flux density will be zero. Continuing along the airgap, the magnetic flux density will climb to a peak, and then drop back down to zero, then climb to a negative peak, and then return to zero. A graph of the flux density versus air gap position would be a sine wave.
The greater the flux density, the greater the torque produced by a given current in the rotor windings. As resistance losses scale with the square of current flow in the windings, the greater the flux density, the lower the resistance losses in the motor. The production of the magnetic flux itself requires current flow, thus there is an ideal maximum flux density for a given operation which minimizes total current flow.
AC induction motors make use of ferromagnetic materials to increase the flux density produced by a given magnetizing current flow. By reducing the current levels needed to produce high flux densities, machine efficiency and performance are greatly enhanced. One difficulty is introduced by the fact that ferromagnetic materials do not have a linear relation between magnetizing current flow and flux densities produced. Specifically, ferromagnetic materials exhibit ‘saturation’, in which increases in magnetizing current produce only slight increases in flux density. Because of the sinusoidal flux distribution used in three phase motors, a portion of the ferromagnetic materials will be near saturation while the majority of the ferromagnetic materials will be well below saturation.
The rotating field produced by the stator windings is complex and irregular. By the principal of superposition, the rotating field may be analyzed as being composed of numerous rotating fields of different shape, including a fundamental or desired lowest frequency structure. The rotating field is composed of this fundamental field and higher frequency harmonic fields.
The excitation currents may similarly be complex, and may be analyzed as being composed of several different harmonic currents. The fundamental excitation current is the primary source of torque.
Spatial harmonics, or air-gap harmonics, are harmonic fields generated by the non-sinusoidal nature of the field generated by each winding. When spatial harmonics are excited by the fundamental drive currents, they produce a secondary rotating field that rotates slower than the fundamental field. For a given excitation frequency, spatial harmonic fields rotate more slowly than the fundamental field.
Harmonic fields generated by non-sinusoidal drive wave-forms are termed temporal harmonics. Rotating fields produced by temporal harmonic currents rotate more rapidly than the fundamental field. When temporal harmonics excite the fundamental spatial field, they produce a secondary rotating field that rotates more rapidly than the fundamental field and may rotate in the opposite direction to the fundamental field.
Therefore, both spatial and temporal harmonics in rotating fields may adversely affect the efficiency of a conventional rotating induction apparatus, lowering torque and increasing current flow.
Early three phase motors used inverters known as six step inverters, to synthesize sine waves for two or three phases. These inherently had a fixed number of pulses per cycle, and often worked with the commutation of one phase on, at the same time rendered a second phase “off”. Improvements to this inverter resulted in the 18-step inverter, which offered greater accuracy, but similarly, each cycle was locked to containing 18 steps. By the way the system was designed, there was a fixed number of pulses per cycle.
More recently, Pulse Width Modulation (PWM) has become the norm, in which a fixed pulses are modulated for each phase to achieve a desired sinusoid.
Usage of pulse width modulation (PWM) in the synthesis of electrical power for motor drive use has certain limitations. Firstly, in order to calculate a desired output amplitude, a base PWM frequency is used, and for each PWM period, the controller uses a technique to calculate the desired output amplitude, to synthesize a desired sine wave, relative to the PWM frequency used.
The amplitude may be selected using table look-up techniques, or using transforming techniques, etc. However, in general, the PWM frequency is fixed, (or independently adjustable,) and remains fixed during motor operation. Sometimes, the PWM frequency may be adjusted, such as by a potentiometer, but this is without any synchronization with the actual waveform frequency at the time.
The problem with this approach is that along with the synthesis of the desired output, there is a substantial amount of random noise, caused by the pulsing carrier wave, which reduces the fidelity of the output.
Another issue common to PWM, is the limitations inherent in sine look-up tables. The PWM controller synthesizes current of a desired output, sometimes by calculating the sine of angles, but usually with reference to a sine look-up table. When calculation is used, no angle error is introduced into the value. However, look up tables often incur substantially less computational expense, and permit the synthesis of complex waveforms.
Look-up tables commonly contain 2 to the power of n entries. When the angle for which a sine is desired happens to correspond exactly to one of the sine table entries, then the correct sine value is returned. For all other angles, an error is introduced. The extent of error to which sines are subject to is largely related to the number of entries in the look-up table. As the number of entries increase, the error is reduced, however this uses additional computational resources. In, for example, a 256 entry sine look-up table, the maximum error will be {fraction (1/512)} of a cycle, with the average error on the order of {fraction (1/1024)} of a cycle. The error is essentially uncorrelated, and will in general be different for each phase of a polyphase system. This causes a phase imbalance.